07930:
Make your circles, then:
Turn on smart guides w/ Ctrl+U, this will give you feedback to know when the pen tool is snapping to an anchor.
P for pen tool, then click on anchor 1, then anchor 2.
Finally, make this a compound path by selecting the two circles and the connecting line hitting Ctrl+8 to make them a compound path.
To answer your second question, no, two paths cannot be *joined* like that, in the sense that the
closed circles do not have an open anchor point to allow a join (Ctrl+J)with the connecting line, (by their nature of being closed.) However, if you
cut the circles at your chosen anchors, you can then join the connecting line to them, but it is necessary to temporarily nudge 1 of the 2 resultant anchors some distance, otherwise your selection will encompass 3 points, and the join command (Ctrl+J) will fail.
All that said, it is not necessary to
join them in your example (join is an Illustrator technical word,) but only to
compound them, unless you are then (for example) going to OPEN up the circles somewhere along their length and apply a pattern stroke to the new contiguous path.
Sef.
It is alright to decorate construction, but never construct decoration. - Pugin, on Arch.